DTIC ADA1025812: Inverse Problem for the Vibrating pdf

DTIC ADA1025812: Inverse Problem for the Vibrating

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We consider the problem of reconstructing the flexural rigidity r(x) and the density rho(x) of a beam. The unknown beam is assumed to have a free left end and a clamped right one. The data consist of the displacement and angle of the center line of the free left end following an initial impulse. The information content of this seismogram-like impulse response is equivalent to three spectra (omega sub n), (nu sub n), (mu sub n) and two gross constants F1, F2. This data do not specify the structure of the vibrating beam uniquely, but rather a class of beams. All the beams in this class share the same structure over the portion of their length which is actually set in motion; they can differ over the portion which is stationary. A method for constructing r(x) and rho(x) is presented. It consists of two steps: first rho(x) and r(x) are determined over a small interval (0,x) adjacent to the free left end.

Next, this known portion of the beam is stripped-off and the response of the resulting truncated beam is computed via the initial data. The procedure is then repeated. Finally, the question of the existence of a solution is discussed. More specifically, conditions on (omega sub n), (nu sub n), (mu sub n) are given which insure that r(x) and rho(x) are physically meaningful. (Author

• Creator/s: Defense Technical Information Center
• Date: 1/1/1979
• Year: 1979
• Book Topics/Themes: DTIC Archive, Barcilon, Victor, CHICAGO UNIV IL DEPT OF GEOPHYSICAL SCIENCES, *MATHEMATICAL MODELS, *VIBRATION, *BEAMS(STRUCTURAL), STIFFNESS, ELASTIC PROPERTIES, EIGENVALUES, KERNEL FUNCTIONS, COEFFICIENTS, BOUNDARY VALUE PROBLEMS, EXPONENTIAL FUNCTIONS, GREENS FUNCTIONS, RAYLEIGH WAVES, DERIVATIVES(MATHEMATICS

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